Two metallic rings $A$ and $B$, identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings $A$ and $B$ jump to heights $h_A$ and $h_B$, respectively, with $h_A>h_B$. The possible relation(s) between their resistivities and their masses $m_A$ and $m_B$ is(are)
Select ALL correct options:
A
$\rho_{\mathrm{A}}>\rho_{\mathrm{B}}$ and $\mathrm{m}_{\mathrm{A}}=\mathrm{m}_{\mathrm{B}}$
B
$\rho_{\mathrm{A}}<\rho_{\mathrm{B}}$ and $\mathrm{m}_{\mathrm{A}}=\mathrm{m}_{\mathrm{B}}$
C
$\rho_{\mathrm{A}}>\rho_{\mathrm{B}}$ and $\mathrm{m}_{\mathrm{A}}>\mathrm{m}_{\mathrm{B}}$
D
$\rho_{\mathrm{A}}<\rho_{\mathrm{B}}$ and $\mathrm{m}_{\mathrm{A}}<\mathrm{m}_{\mathrm{B}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
Solution
As $-\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{emf}$ is same, the current induced in the ring will depend upon resistance of the ring. Larger the resistivity smaller the current.
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